Emergent Spacetime Rigidity and the Regularization of the Big Bang Singularity (v2)

We extend the concept of emergent spacetime rigidity to the early Universe, applying it to the Big Bang singularity. In standard Friedmann–Robertson–Walker (FRW) cosmology, curvature invariants diverge as t → 0. Rigidity prevents such divergences: the Kretschmann scalar and the Ricci scalar saturate at the Planck scale, replacing the singularity with a finite core. These bounds are structural rather than dynamical: they express an intrinsic limitation of curvature, independent of matter content. This leads to a natural regularization of the Big Bang, with entropy and density bounded by holographic principles. The framework highlights the dimensionless suppression factor R = (H t_P)2. At the present epoch, R0 ≈ 1.4×10−122, quantitatively bridging Planck physics and the observed vacuum energy. The model suggests that the Universe is born from a finite-entropy seed and evolves under an irreversible entropic flow, consistent with the Second Law of thermodynamics. Unlike other bounce scenarios that rely on additional assumptions, in the rigidity framework stability follows automatically from the curvature bound itself. The bounce is therefore not only non-singular but also dynamically robust, ensuring that perturbations cannot destabilize it. This dual outcome — singularity resolution and automatic stability — highlights the structural consistency of rigidity in cosmology. It provides a natural foundation for connecting the early-universe bounce to the same principle that explains dark energy at late times